[FOM] Counterfactuals in relative computability theory

[Matthias Jenny]

On Thu, Aug 18, 2016 at 11:26 PM Timothy Y. Chow <tchow at alum.mit.edu> wrote:

>
> The point is that I don't see how you're arriving at the conclusion that
> "algorithm" is rigid.  If you were to say, "The name `Barack Obama' is
> rigid," then I would presume that you're simply agreeing with Kripke's
> view of names.  But "algorithm," on the face of it, is not a name.
> You're saying that it "picks out" an "abstract object" but I don't quite
> understand this either since there are different ways of "picking out"
> objects that have radically different behavior when you move across
> possible worlds.
>

I'm afraid I still don't understand why we're talking about 'algorithm'
instead of about algorithms. My claim is that algorithms are necessary
existents (if they exist, they exist necessarily, and if they don't, they
couldn't exist). The semantics of 'algorithm' seems to me to be besides the
point. Furthermore, I think it strikes me as distracting to talk about
whether 'algorithm' is rigid in the way Kripke says proper names are. For
even if we accept that proper names are rigid, this is usually put as
follows: A proper name refers to the same individual in every possible
world *in which the name has a referent*. This is to accommodate the fact
that most individuals aren't necessary existents.


>
> Further complicating the matter is that you are arguing that "algorithm"
> is "fully precise" but perhaps not "mathematically precise" because the
> latter concept is unclear to you.  You maintain this even though by far
> the majority view in discussions of the Church-Turing thesis is that the
> side of the equation with the word "algorithm" (as opposed to the other
> side, which involves "Turing machine") is informal and *not* precise.  So
> I don't know what you mean by "fully precise" if it's not the same as
> "mathematically precise."
>

The reason why I was hesitant to use the expression 'mathematically
precise' is because, as I've tried to explain, the way you use this
expression seems to me to pick out an epistemological property and not an
ontological one.

Also, with all of that said, I wanted to remind you that my argument
involving the idea that algorithms are necessary existents is only one of
two arguments for the necessity of the Church-Turing thesis.
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